Subsets where each chosen letter may be marked bold

Erica forms a set $T$ by choosing elements from the six-letter set $S=\{I,J,K,L,M,N\}$. For any element she is unsure about, she includes it in $T$ but writes it in bold. Valid results include $\{K\}$, $\{\mathbf{L},M\}$ and $\{I,\mathbf{J},\mathbf{N}\}$; an element may not appear both plain and bold, so $\{M,\mathbf{M}\}$ is not allowed. How many different sets $T$ can she write?

$729$. Each of the six elements independently has three states: left out, included plainly, or included in bold. That gives $3^6=729$.